Regard an n x n matrix as a point

Regard an n x n matrix as a point in the -fold product Rn x . x Rn by considering each row as a member of Rn..
a. Prove that det : Rn x . x Rn → Rn is differentiable and
b. If aij : R →R are differentiable and f(t) = det (aij(t)), , show that